Approximate bound states of the Dirac equation with some physical quantum potentials

TL;DR

This paper derives approximate analytical solutions for the Dirac equation with specific quantum potentials, providing bound state energies and wavefunctions under spin and pseudospin symmetry using the Nikiforov-Uvarov method.

Contribution

It introduces a new analytical approach to solve the Dirac equation with reflectionless and Rosen-Morse potentials under symmetry conditions.

Findings

Bound state energy spectra obtained analytically.

Wavefunctions for upper and lower spinors derived.

Special cases like s-wave and non-relativistic limits discussed.

Abstract

The approximate analytical solutions of the Dirac equations with the reflectionless-type and Rosen-Morse potentials including the spin-orbit centrifugal (pseudo-centrifugal) term are obtained. Under the conditions of spin and pseudospin (pspin) symmetry concept, we obtain the bound state energy spectra and the corresponding two-component upper- and lower-spinors of the two Dirac particles by means of the Nikiforov-Uvarov (NU) method in closed form. The special cases of the s-wave {\kappa}=\pm1 (l=l=0) Dirac equation and the non-relativistic limit of Dirac equation are briefly studied.